Strain-Programmable Fiber-Based Artificial Muscle

Abstract

Artificial muscles may accelerate the development of robotics, haptics, and prosthetics. Although advances in polymer-based actuators have delivered unprecedented strengths, producing these devices at scale with tunable dimensions remains a challenge. We applied a high-throughput iterative fiber drawing technique to create strain-programmable artificial muscles with dimensions spanning three orders of magnitude. These fiber-based actuators are thermally and optically controllable, can lift more than 650 times their own weight, and withstand strains of >1000%. Integration of conductive nanowire meshes within these fiber-based muscles offers piezoresistive strain feedback and demonstrates long-term resilience across >10⁵ deformation cycles. The scalable dimensions of these fiber-based actuators and their strength and responsiveness may extend their impact from engineering fields to biomedical applications.

One Sentence Summary:

Iterative fiber drawing enables strain-programmable artificial muscles scalable across three orders of magnitude.

Linear actuators simultaneously offering high temporal responsiveness, power-to-mass ratio, and strain and capable of operating across micrometer to centimeter spatial scales are poised to advance the fields of robotics, prosthetic limbs, and transportation (1). Although actuators based on shape-memory alloys (2), stimuli-responsive polymers (3–9), and carbon composites (10–14) offer light-weight, compact, and cost-effective alternatives to traditional hydraulic, pneumatic, and servo designs, their temporal responsiveness remains limited (15, 16). Recent research in polymer and composite actuators has drawn inspiration from cucumber tendrils that rely on differential swelling within their compartments to achieve high power-to-mass ratios and strains (17–20). Producing such structures at scale with tunable dimensions, however, presents a challenge. Furthermore, low-latency linear actuation without secondary transduction and integration of feedback mechanisms within these fiber-based artificial muscles has not been demonstrated (21).

We reasoned that differential thermal expansion within polymer bimorph structures comprising an elastomer and a thermoplastic polymer (22–24) amplified by the tendril-like spring geometry (Fig. S1) would allow for linear actuation at low thermal stimuli. To produce bimorph structures with arbitrary lengths and lateral dimensions ranging from microns to millimeters we relied on a scalable fiber drawing process (25). Thermal drawing enables lateral size reduction of preforms by factors of 10¹-10⁵ via controlled application of heat and tension while simultaneously delivering meters to kilometers of fiber (23, 26, 27). Unlike other fiber fabrication techniques such as electro- and jet-spinning, thermal drawing is applicable to multiple materials with a diversity of non-cylindrical geometries (27). To be compatible with thermal drawing the layers of the bimorph must, however, be composed of materials with similar viscosities at the drawing temperature. Simultaneously, maximizing the differences in thermal expansion coefficients (α) is necessary to achieve robust actuation. Guided by these constraints, a high-density polyethylene (PE, melting temperature T_m = 120 °C, α = 1.3×10⁻⁴ K⁻¹) and cyclic olefin copolymer elastomer (COCe, melting temperature T_m = 84 °C, α = 2.6×10⁻⁵ K⁻¹) were chosen as the constituents of the bimorph fibers (Table S1). Finite element analysis was then applied to select a cross-sectional geometry that would optimize the thermal responsiveness of the bimorphs (Fig. S2 and Table S2). The final design of the bimorph fibers comprised identical PE and COCe layers with rectangular cross sections (25).

These fibers were then drawn from preforms composed of COCe and high-density PE blocks (25×8 mm² cross section, 200 mm long) joined within a poly(methyl methacrylate) (PMMA) cladding (35×26 mm² outer cross-sectional dimensions) (Fig. 1A, Fig. S3). Prior to drawing, the preforms were annealed under pressure of 50 bar and temperature of 125 °C to promote adhesion between the PE and COCe layers. By setting the drawing temperature (290–310 °C) and the relative feed (v_f = 1 mm/ min) and draw (v_d = 2 – 3 m/ min) speeds, the cross-sectional area of the fiber was tuned between 50×35 μm² and 5×3.5 mm² over a 500 m length (Fig. 1B). To further reduce the lateral dimensions, the fibers produced by the first drawing step were stacked within another PMMA preform and drawn at similar conditions to produce COCe/PE bimorph elements with cross-sectional areas as low as 13×8 μm² (Fig. 1A, Fig. S4). The thermomechanical mismatch between COCe and PE set an upper limit of processing 20 first-step fibers for every second-step PMMA preform. Increasing the number of fibers resulted in contraction failure of the preform (Fig. S5). Following drawing, the PMMA cladding was mechanically stripped to release the bimorph structures (Fig. 1C). The tension (70–100 mN) experienced by the fibers during drawing led to the formation of a spring-like shape upon PMMA cladding removal (coil diameter ~30–40 mm, Fig. S6).

Fig. 1. Fabrication, and morphological characterization.

(A) Bimorph fibers produced via two-step thermal drawing. HDPE = high density PE. (B), A photograph of ~60 m of PMMA-encapsulated bimorph fibers. (C) An illustration of the PMMA cladding removal. (D) Cross-sectional scanning electron microscope (SEM) images of a fiber prior to and following cold drawing. Inset: COCe structure after stretching (Scale bar: 20 μm). (E) Cold drawing process to obtain a spring actuator. Steps 1 to 4 show the stretching process. Upon release, shown in steps 5 to 8, the fibers formed springs. (F and G) Micrographs and photographs of the first-step and second-step artificial muscles (Scale bars in F: 200 μm). (H) Fiber-based muscle contracting in response to temperature increase of ΔT=14 ^oC (spring index: k = 4.70, 6 turns/cm).

To produce actuated springs via strain-programming from the bimorph fibers, these structures were cold drawn at strains of 50–1300%, which induced plastic deformation in PE (Fig. 1D). Upon release, the elastomeric COCe component attempted to contract to its original dimensions and the resulting stress in the bimorph structure induced the formation of tendril-like springs (Fig. 1E, Movies S1 and S2). The high pre-strains between ~700–1300% were only tolerated by a subset of fibers, likely due to the manufacturing defects. The diameters of springs scaled with the cross-sectional dimensions of the precursor fibers, and a variety of springs could be obtained from the first and second iterative draws (Fig. 1F–G) (25).

The five-fold mismatch in coefficients of the thermal expansion between the COCe and PE enabled rapid thermal actuation. Upon temperature increase, the PE underwent greater thermal expansion relative to COCe, which increased the tensile strain in COCe and induced further tightening of the springs (Fig. S7) (25). Fig. 1H demonstrates a 50% linear contraction in a fiber actuator with a 0.64×1 mm² cross-sectional area in response to a temperature increase of ΔT=14 °C applied over 4 s.

We observed the spontaneous formation of unstable bifurcations, which are also found in cucumber tendrils and termed “perversions” by Darwin (28). The stochastic formation of these bifurcations is predicted by applying the Kirchhoff theory for thin rods to the fibers with elliptical cross sections (Fig. S7–9) (19, 25). Although these structures do not significantly impede the thermal actuation performance, their formation could, at least in part, be circumvented by simultaneously releasing the ends of the fibers following the application of pre-strain (25).

To optimize the thermal actuation performance, we investigated the effects of cold drawing parameters applied to COCe/PE bimorph fibers on the mechanical properties of the resulting fiber-based muscles. While fibers composed of PE and COCe alone exhibited stress-strain characteristics of a tough plastic and an elastomer, respectively, the bimorph fibers exhibited intermediate behavior (Fig. 2A) (23, 29). Increasing the deformation rate from 10 mm/min to 50 mm/min during the cold drawing of the bimorph fibers allowed for greater built-in strain within the resulting artificial muscles. Further increasing the deformation rate, however, reduced the amount of achievable strain (Fig. 2A). This was consistent with an increase in the yield strength and the elastic modulus in thermoplastic materials with increasing deformation rate (29, 30). For a given fiber, the spring diameter and the spring index of the actuators formed by cold drawing were controlled by the deformation rate and the maximum applied strain (Fig. 2B–D). Consistent with the maximum allowable strain observed at 50 mm/min for fibers with 300×470 μm² cross-sectional area, the spring diameters reached their minimum at this deformation rate (Fig. 2B). At a fixed deformation rate, increasing the strain applied to bimorph fibers during cold drawing produced actuators with smaller spring diameters and a greater number of turns per centimeter (Fig. 2C). Spring index (k) of the actuators increased with the spring diameter and the actuation strain (Fig. 2D) resulting in higher work capacity (Fig. 2E). The latter was limited by the coil-to-coil contact at the highest actuation temperature. An increase in the pre-strain decreased the spring diameter, and thus the spring index. Decreasing cross-sectional dimensions of the fibers yielded an increase in residual stress in the springs formed following the cold drawing process (Fig. 2F).

Fig. 2. Mechanical characterization of fiber-based artificial muscle.

(A) Stress-strain curves recorded at different extension rates for precursor fibers (without PMMA cladding) with a cross-sectional area of 300×470 μm². (B) Change in the spring diameter with respect to the deformation rate. (C) Spring diameter and number of coils versus applied pre-strain. Error bars and shaded areas represent average and standard deviation, respectively. The number of samples n=5. (D) Change in the spring index with respect to spring diameter and actuation strain. (E) Change in the actuation stress-strain (grey) and work capacity (green). Attributes of the fibers are k=6, 6 turns/cm (continuous line); k=5, 10 turns/cm (dashed line); k=5.5, 12 turns/cm (dot line). (F) Change in the residual stress with respect to the cross-sectional area. (G) The setup used for the force measurement of the fibers with 300×470 μm² cross-section (scale bar is 5 mm). For the fibers with a 8×12.5 μm² cross-section (scale bar is 200 μm), a similar setup was used. The optical heat source was replaced with a micro-Peltier heater and a force gauge had a higher resolution. (H) Temperature and force responses to photothermal pulses collected for a fiber with 300×470 μm² cross-section (k=5, 8 turns/cm). (I) Generated force vs. the temperature difference (number of cycles 300) for fibers with 200×312 μm² cross-section (k=5, 10 turns/m). Navy blue, cerrulean blue, cyan, and green data point clusters represent different temperature ranges of 3.32±0.26 °C, 5.28±0.37 °C, 9.74±0.34 °C, and 12.98±0.74 °C, respectively. (J) Temperature and force responses to thermal pulses for a fiber with an 8×12.5 μm² cross-section (k=4.6, 60 turns/cm). (K) Change in the efficiency with respect to actuation strain (blue line k=6, 6 turns/cm; green line k=5, 10 turns/cm; grey line k=5.5, 12 turns/cm). (L) Force measured across 300 thermal actuation cycles applied over 3 consecutive days for a fiber with 200×312 μm² cross section (k= 5, 10 turns/cm). Inset: A single actuation cycle.

The force generated by the cold-drawn (maximum strain of 700%, 50 mm/min deformation rate) fiber-based muscles with cross-sectional areas of 300×470 μm² was characterized by connecting the devices to a force gauge within a custom designed characterization setup (Fig. 2G, Fig. S10).

A modulated broadband light supplied thermal stimuli, and a thermistor was placed near the fiber muscles to monitor the change in the temperature concurrent with the generated force measurements. Three-second illumination pulses separated by 10 s rest periods induced temperature gradients of 3.45±0.43 °C/s (n=6 cycles), causing a force of 36.23±5.42 mN in 5 cm long fiber muscles (Fig. 2H). An actuation rate of 13.25±1.66 N/s for a temperature increase rate of 1.11±0.12 °C/s and a power-to-mass ratio of 75 Wkg⁻¹ surpassed the average human muscle (50 Wkg⁻¹). Increasing the exposure times led to a proportionate increase in both heating and generated force (Fig. 2I). No decline in performance was observed across multiple actuation cycles at different temperatures (Fig. 2I). Artificial muscles produced from the miniature bimorph fibers with cross-sectional areas of 8×12.5 μm² fabricated via the two-step thermal drawing were similarly evaluated for their actuator performance (Fig. 2G, J and Fig. S11 and S12). A micro-Peltier was used to apply a thermal stimulus and a thermistor was placed near the fiber muscles to monitor the change in the temperature concurrent with the generated force measurement (Fig. S13). A temperature gradient of 11.09±0.55 °C/s (n=10 cycles) produced a force of 371±40.7 μN in these 5 mm fiber muscles. The actuation rate of the miniature fiber muscle was 6.33±0.72 N/s for a temperature increase rate of 130.3±16.9 °C/s and the power-to-mass ratio was calculated as 90 Wkg⁻¹. The power efficiency of the fiber-based muscles was found to increase with actuation strain and was higher for the fibers with larger cross-sectional areas (Fig. 2K). Actuator performance attributes of the fiber-based muscles are summarized in Table S3. The devices (5 cm long, cross-sectional area 300×470 μm²) were subjected to 300 cycles of thermal actuation over 3 consecutive days (ΔT=13 °C for 6 s, followed by 30 s rest, Fig. 2L), and no decline in performance was observed.

Fiber-based muscles were outfitted with conductive meshes of silver nanowires (AgNW, diameter = 70 nm and length = 50 μm) to enable monitoring of their contraction and elongation, These meshes were deposited directly onto the surfaces of the fiber muscles following the cold drawing process of the bimorph fibers, which was followed by the deposition of a protective stretchable layer of polydimethylsiloxane (PDMS) elastomer (23). Since percolation within the AgNW mesh changes with the contraction or elongation of the underlying substrates, AgNW-coated fiber muscles act as piezoresistive sensors of deformation in response to stimuli. To evaluate this sensing ability, one end of the fiber muscles was connected to a direct current (DC) motor, and the resistance change was recorded by a voltage divider (Fig. 3A). A fractional resistance change of 0.47% was repeatable across ~12000 cycles of 20% elongation (Fig. 3B–D). While a slow increase in baseline resistance was observed (Fig. 3B, C), the relative change between extension and release cycles remained stable (Fig. 3D).

Fig. 3. Electrical feedback in fiber-based artificial muscle.

(A) A schematic illustration of the setup for the resistance measurements for fibers with 300×470 μm² cross-sectional area (k = 5, 8 turns/cm). Inset: A SEM image of silver nanowire mesh on the surface of a 300×470 μm² fiber-based muscle. (B) Resistance waveforms collected at different numbers of extension and release cycles. (C) The change in the extended and released resistance for ~12000 cycles. (D) Hysteresis curve showing the resistance vs. the applied strain for a single cycle of deformation. The lines represent average and error bars represent the standard deviation.

A single 5 cm long fiber muscle with a cross-sectional area of 300×470 μm² was able to lift a 1g weight by 5.12±0.76 mm (12% strain) in response to a thermal stimulus of ΔT=10 °C (from room temperature) delivered by a heat gun (Fig. 4A, B and Movie S3). This behavior was reversible and repeatable across multiple cycles of 2 s heat pulses separated by 6 s rest periods, during which the fiber muscle cooled down to room temperature (Fig. 4C). The vertical displacement was linearly correlated with the thermal gradient (Fig. 4D). Permanent deformation was observed for temperature gradients ΔT≥50 °C consistent with the thermomechanical properties of PE and COCe. Repeated application of 100 cycles of thermal actuation (ΔT=8.8±0.6 °C) delivered reproducible actuation strains (10.1±1.5%, Fig. 4E). While an additive boost in strength was afforded by bundling multiple fibers in an oblique fashion, no observable change in stretchability was observed (Fig. 4F, Fig. S12, and Movie S4).

Fig. 4. Thermal actuation of fiber-based muscles.

(A) Schematic illustration of the vertical lift experiment, where t is time, m is mass, and Δx is displacement. (B) A photographic time series collected during a displacement experiment in (A). The heat was applied in 2 s pulses separated by 6 s rest epochs. The load mass is 1 g. (C) Waveforms for the heat pulses (top), the corresponding change in the temperature at the fiber surface (middle), and the displacement of the 1g load. (D) The vertical displacement Δx of a 1g load in response to temperature increase ΔT. (E) Strain measurement across 100 cycles of thermal actuation. (F) The maximum displacement for fiber bundles loaded with weights 1, 2, 3, 4, 5, 10, 50, 100, and 200 g. (G) A printed model of a weight-lifting artificial limb, inspired by a human arm. (H) A photographic time series of the artificial limb lifting a 1g load. The heat was applied using a heat gun for 2 s and then followed by 5 s rest epochs. (A-G) Fiber cross-sectional area is 300×470 μm², spring index k = 5, and the number of turns per cm is 8. (I) The change in the fiber length, a piezoresistive strain feedback signal, and the angle of the arm for the experiment in (H).

To further illustrate the potential application of the fiber-based muscle as a model of biological muscle, we designed and printed a weight-lifting artificial limb inspired by a human arm (Fig. 4G). One end of the fiber muscle (300×470 μm² cross section) was then affixed to the radius and ulna of the model forearm, while the other end was affixed to the clavicle. As found in the human arm, the joint between the humerus and the forearm was aligned with the clavicular muscle connection slot to maximize the displacement corresponding to a given bicep contraction (31). The artificial bicep was actuated by 2 s heat pulses (ΔT=10 °C) delivered by a heat gun, and relaxed upon cooling to room temperature (Fig. 4H and Movie S5). The change in an angle between the forearm and humerus during operation correlated linearly with the fiber muscle contraction and extension (Fig. 4I). A miniature arm was used to lift a 1 g dumbbell, and the platform was scalable to a larger limb with greater weightlifting performance of 2 g afforded by 2 parallel fibers (Movie S6).

This work presents a scalable strategy to produce fiber-based actuators with lateral dimensions ranging from millimeters to microns and arbitrary lengths. Cold drawing bimorph fibers composed of PE and COCe formed springs with the spring index and residual stress determined by the fiber cross-sectional dimensions, and the applied strain and deformation rate. The mismatch in the thermo-mechanical properties enabled reversible and repeatable thermal actuation. Conceptual demonstrations of load bearing and joint manipulation facilitated by the fiber-based artificial muscles indicate the possibility of their future applications in robotics and prosthetic limb technologies